Require packages

library(utils)
library(dplyr)
library(ggplot2)
library(maps)
library(stringr)
library(readr)
library(tidyverse)
library(readxl)
library(plotly)
library(MASS)
library(kableExtra)
library(broom)
library(stargazer)
library(ggfortify)

Cleaning Data

#read the Dataset sheet into “R”. The dataset will be called "data".
data <- read.csv("https://opendata.ecdc.europa.eu/covid19/casedistribution/csv", na.strings = "", fileEncoding = "UTF-8-BOM")

#library("dplyr") require "dplyr" package for the use of %>%
covid.data = data %>%
  rename(Date="dateRep") %>%
  rename(Region="countriesAndTerritories") %>%
  mutate(Date=as.Date(Date,format="%d/%m/%y"))%>% 
  mutate(Region = str_replace_all(Region, "_", " "))%>% 
  group_by(Region) %>%
  mutate(cases_Diff = lag(cases)-cases) %>%
  mutate(deaths_Diff = lag(deaths)-deaths) %>% 
  relocate(cases_Diff, .after = cases) %>%
  relocate(deaths_Diff, .after = deaths) %>%
  drop_na(countryterritoryCode)

Data Summary

#population dataframe
pop.data = unique(data.frame(covid.data$Region,covid.data$popData2019,covid.data$continentExp,covid.data$countryterritoryCode))
names(pop.data)=c("Region","Population2019","Continents","Codes")
pop.data = na.omit(pop.data)
pop.data = unique(pop.data)

#cases dataframe
case.data = data.frame(covid.data$Region,covid.data$cases,covid.data$countryterritoryCode) 
names(case.data) = c("Region","cases","Codes") 
case.data=aggregate(case.data$cases, by=list(Category=case.data$Region), FUN=sum)
case.data = as.data.frame(cbind(case.data,unique(covid.data$countryterritoryCode)))
names(case.data) = c("Region","cases","Codes")
case.data = na.omit(case.data)

#death dataframe
death.data = data.frame(covid.data$Region,covid.data$deaths,covid.data$countryterritoryCode) 
names(death.data) = c("Region","deaths","Codes") 
death.data=aggregate(death.data$deaths, by=list(Category=death.data$Region), FUN=sum)
death.data = as.data.frame(cbind(death.data,unique(covid.data$countryterritoryCode)))
names(death.data) = c("Region","deaths","Codes")
death.data = na.omit(death.data)

#Death/Case dataframe
death_case.data = data.frame(case.data$Region,death.data$deaths/case.data$cases,case.data$Codes)
names(death_case.data) = c("Region","Deaths/Case Ratio","Codes")

#death/pop *100
death_pop.data = data.frame(pop.data$Region,death.data$deaths/pop.data$Population2019*100,pop.data$Codes)
names(death_pop.data) = c("Region","Values","Codes")

#Land Area
Land_Area <- read_excel("Land Area.xls")
names(Land_Area) = Land_Area[3,]
Land_Area = Land_Area[-(1:3),]
Land_Area = Land_Area[,c(1,2,62,63)]

#Complete 2018
for (i in 1:nrow(Land_Area)) {
  if(is.na(Land_Area$`2018`[i])){
    Land_Area$`2018`[i] = Land_Area$`2017`[i]
  }
}
Land_Area = na.omit(Land_Area)[,-3]
names(Land_Area)[3] = "Area"

combine = full_join(pop.data, Land_Area, by=c("Codes"="Country Code"))
combine = na.omit(combine)[,-5]
pop.square = na.omit(combine)
pop.square$Area = as.numeric(pop.square$Area)

Ploting data

#Population Ditribution
pop.fig <- plot_ly(pop.data, type='choropleth', locations=pop.data$Codes, z=log2(pop.data$Population2019), text=pop.data$Region, colorscale="Blues",reversescale =T)%>%
  layout(title = 'The Logarithm of World Population in 2019')%>%
  colorbar(title = "Population Rates",limits = c(15,31))
pop.fig
#Population Density Ditribution
pop.square.fig <- plot_ly(pop.square, type='choropleth', locations=pop.square$Codes, z=log(pop.square$Population2019/pop.square$Area), text=pop.square$Region, colorscale="Blues",reversescale =T)%>%
  layout(title = 'The Logarithm of World Population Density in 2019')%>%
  colorbar(title = "Density Rates",limits = c(-2,7))
pop.square.fig
#Case Ditribution
case.fig <- plot_ly(case.data, type='choropleth', locations=case.data$Codes, z=log2(case.data$cases), text=case.data$Region, colorscale="Reds",reversescale =F)%>%
  layout(title = 'The Logarithm of World Covid-19 Cases Number')%>%
  colorbar(title = "Cases Number",limits = c(4,24))
case.fig
#Death Ditribution
death.fig <- plot_ly(death.data, type='choropleth', locations=death.data$Codes, z=log2(death.data$deaths+1), text=case.data$Region, colorscale="Reds",reversescale =F)%>%
  layout(title = 'The Logarithm of World Covid-19 Deaths Number')%>%
  colorbar(title = "Deaths Number")
death.fig
#Death/Case Ditribution
death_case.fig <- plot_ly(death_case.data, type='choropleth', locations=death_case.data$Codes, z=death_case.data$`Deaths/Case Ratio`, text=death_case.data$Region, colorscale="Reds",reversescale =F)%>%
  layout(title = 'The Ratio of World Covid-19 Deaths to Cases Number')%>%
  colorbar(title = "Ratio Number",limits = c(0,0.1))
death_case.fig
#Death/pop*100 Ditribution
death_pop.fig <- plot_ly(death_pop.data, type='choropleth', locations=death_pop.data$Codes, z=death_pop.data$`Values`, text=death_pop.data$Region, colorscale="Reds",reversescale =F)%>%
  layout(title = 'The Ratio of World Covid-19 Death/Population*100')%>%
  colorbar(title = "Ratio Number")
death_pop.fig

Modeling Preparation

#Creat Density Variable
pop.density = pop.square %>%
  mutate(Density = Population2019/Area)
pop.density = pop.density[,c(4,6)]
#Creat data for time series
covid.time = covid.data[,c(1,6,8:9,11:12)]%>%
  rename(Codes="countryterritoryCode")%>%
  inner_join(pop.density)%>%
  mutate(Region = as.factor(Region))%>%
  mutate(group_id = as.integer(Region))
groups = length(unique(covid.time$Region))

#Lag cases and deaths Difference
for (k in 1:14) {
  CASE=NULL
  for (j in 1:groups) {
    CASE=c(CASE,lag(covid.time$cases_Diff[covid.time$group_id==j],k))
  }
  covid.time = cbind(covid.time,CASE)
}
names(covid.time)[9:22]=paste("CASE_DIFF",1:14,sep="-")

for (k in 1:14) {
  DEATH=NULL
  for (j in 1:groups) {
    DEATH=c(DEATH,lag(covid.time$deaths_Diff[covid.time$group_id==j],k))
  }
  covid.time = cbind(covid.time,DEATH)
}
names(covid.time)[23:36]=paste("DEATH_DIFF",1:14,sep="-")

Modeling

#Cases on Cases
data1 = covid.time[,c(2,9:22)]
fit1.m1 <- lm(cases_Diff~., data=na.omit(data1))
fit2.m1 <- lm(cases_Diff~1, data=na.omit(data1))

step.m1 = stepAIC(fit2.m1,direction="both",scope=list(upper=fit1.m1,lower=fit2.m1),trace = FALSE)

summary(step.m1)
## 
## Call:
## lm(formula = cases_Diff ~ `CASE_DIFF-7` + `CASE_DIFF-14` + `CASE_DIFF-1` + 
##     `CASE_DIFF-8` + `CASE_DIFF-2` + `CASE_DIFF-9` + `CASE_DIFF-6` + 
##     `CASE_DIFF-12` + `CASE_DIFF-3` + `CASE_DIFF-13` + `CASE_DIFF-4` + 
##     `CASE_DIFF-10` + `CASE_DIFF-5` + `CASE_DIFF-11`, data = na.omit(data1))
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -53130    -25    -16     -4  42720 
## 
## Coefficients:
##                 Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)    15.681509   3.821143    4.104 4.07e-05 ***
## `CASE_DIFF-7`   0.489465   0.004681  104.574  < 2e-16 ***
## `CASE_DIFF-14`  0.114185   0.003600   31.714  < 2e-16 ***
## `CASE_DIFF-1`  -0.552226   0.004227 -130.642  < 2e-16 ***
## `CASE_DIFF-8`   0.356644   0.004777   74.659  < 2e-16 ***
## `CASE_DIFF-2`  -0.419901   0.004742  -88.542  < 2e-16 ***
## `CASE_DIFF-9`   0.212261   0.004955   42.836  < 2e-16 ***
## `CASE_DIFF-6`   0.070500   0.004939   14.275  < 2e-16 ***
## `CASE_DIFF-12` -0.118439   0.004673  -25.344  < 2e-16 ***
## `CASE_DIFF-3`  -0.253793   0.004952  -51.254  < 2e-16 ***
## `CASE_DIFF-13` -0.117971   0.004332  -27.232  < 2e-16 ***
## `CASE_DIFF-4`  -0.145661   0.005046  -28.869  < 2e-16 ***
## `CASE_DIFF-10`  0.077947   0.004875   15.990  < 2e-16 ***
## `CASE_DIFF-5`  -0.074434   0.005050  -14.739  < 2e-16 ***
## `CASE_DIFF-11`  0.014213   0.004820    2.949  0.00319 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 878.7 on 53164 degrees of freedom
## Multiple R-squared:  0.5888, Adjusted R-squared:  0.5887 
## F-statistic:  5437 on 14 and 53164 DF,  p-value: < 2.2e-16
#Cases & Deaths on Cases
data2 = covid.time[,c(2,9:36)]
fit1.m2 <- lm(cases_Diff~., data=na.omit(data2))
fit2.m2 <- lm(cases_Diff~1, data=na.omit(data2))

step.m2 = stepAIC(fit2.m2,direction="both",scope=list(upper=fit1.m2,lower=fit2.m2),trace = FALSE)

summary(step.m2)
## 
## Call:
## lm(formula = cases_Diff ~ `CASE_DIFF-7` + `CASE_DIFF-14` + `CASE_DIFF-1` + 
##     `CASE_DIFF-8` + `CASE_DIFF-2` + `CASE_DIFF-9` + `CASE_DIFF-6` + 
##     `CASE_DIFF-12` + `CASE_DIFF-3` + `CASE_DIFF-13` + `CASE_DIFF-4` + 
##     `CASE_DIFF-10` + `CASE_DIFF-5` + `DEATH_DIFF-8` + `DEATH_DIFF-7` + 
##     `DEATH_DIFF-6` + `DEATH_DIFF-9` + `DEATH_DIFF-5` + `DEATH_DIFF-2` + 
##     `CASE_DIFF-11` + `DEATH_DIFF-10` + `DEATH_DIFF-11` + `DEATH_DIFF-12` + 
##     `DEATH_DIFF-13` + `DEATH_DIFF-14` + `DEATH_DIFF-1`, data = na.omit(data2))
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -53595    -24    -15     -3  41110 
## 
## Coefficients:
##                  Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)     14.572354   3.801912    3.833 0.000127 ***
## `CASE_DIFF-7`    0.464288   0.004828   96.157  < 2e-16 ***
## `CASE_DIFF-14`   0.109556   0.003669   29.858  < 2e-16 ***
## `CASE_DIFF-1`   -0.559992   0.004262 -131.384  < 2e-16 ***
## `CASE_DIFF-8`    0.331329   0.004886   67.818  < 2e-16 ***
## `CASE_DIFF-2`   -0.429274   0.004797  -89.491  < 2e-16 ***
## `CASE_DIFF-9`    0.198530   0.005027   39.491  < 2e-16 ***
## `CASE_DIFF-6`    0.054925   0.005046   10.884  < 2e-16 ***
## `CASE_DIFF-12`  -0.119549   0.004748  -25.180  < 2e-16 ***
## `CASE_DIFF-3`   -0.257402   0.004970  -51.792  < 2e-16 ***
## `CASE_DIFF-13`  -0.121642   0.004406  -27.608  < 2e-16 ***
## `CASE_DIFF-4`   -0.145509   0.005063  -28.742  < 2e-16 ***
## `CASE_DIFF-10`   0.071964   0.004943   14.558  < 2e-16 ***
## `CASE_DIFF-5`   -0.080894   0.005125  -15.785  < 2e-16 ***
## `DEATH_DIFF-8`   2.188295   0.111527   19.621  < 2e-16 ***
## `DEATH_DIFF-7`   1.949829   0.102564   19.011  < 2e-16 ***
## `DEATH_DIFF-6`   1.273209   0.090964   13.997  < 2e-16 ***
## `DEATH_DIFF-9`   1.532828   0.115625   13.257  < 2e-16 ***
## `DEATH_DIFF-5`   0.639008   0.071197    8.975  < 2e-16 ***
## `DEATH_DIFF-2`   0.333297   0.063829    5.222 1.78e-07 ***
## `CASE_DIFF-11`   0.010553   0.004889    2.158 0.030910 *  
## `DEATH_DIFF-10`  1.280985   0.114642   11.174  < 2e-16 ***
## `DEATH_DIFF-11`  1.225222   0.110269   11.111  < 2e-16 ***
## `DEATH_DIFF-12`  1.007917   0.102001    9.881  < 2e-16 ***
## `DEATH_DIFF-13`  0.862914   0.090589    9.526  < 2e-16 ***
## `DEATH_DIFF-14`  0.572329   0.070579    8.109 5.21e-16 ***
## `DEATH_DIFF-1`   0.176808   0.064201    2.754 0.005889 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 874.2 on 53152 degrees of freedom
## Multiple R-squared:  0.5931, Adjusted R-squared:  0.5929 
## F-statistic:  2980 on 26 and 53152 DF,  p-value: < 2.2e-16
#Compare models
anova(step.m1,step.m2)
## Analysis of Variance Table
## 
## Model 1: cases_Diff ~ `CASE_DIFF-7` + `CASE_DIFF-14` + `CASE_DIFF-1` + 
##     `CASE_DIFF-8` + `CASE_DIFF-2` + `CASE_DIFF-9` + `CASE_DIFF-6` + 
##     `CASE_DIFF-12` + `CASE_DIFF-3` + `CASE_DIFF-13` + `CASE_DIFF-4` + 
##     `CASE_DIFF-10` + `CASE_DIFF-5` + `CASE_DIFF-11`
## Model 2: cases_Diff ~ `CASE_DIFF-7` + `CASE_DIFF-14` + `CASE_DIFF-1` + 
##     `CASE_DIFF-8` + `CASE_DIFF-2` + `CASE_DIFF-9` + `CASE_DIFF-6` + 
##     `CASE_DIFF-12` + `CASE_DIFF-3` + `CASE_DIFF-13` + `CASE_DIFF-4` + 
##     `CASE_DIFF-10` + `CASE_DIFF-5` + `DEATH_DIFF-8` + `DEATH_DIFF-7` + 
##     `DEATH_DIFF-6` + `DEATH_DIFF-9` + `DEATH_DIFF-5` + `DEATH_DIFF-2` + 
##     `CASE_DIFF-11` + `DEATH_DIFF-10` + `DEATH_DIFF-11` + `DEATH_DIFF-12` + 
##     `DEATH_DIFF-13` + `DEATH_DIFF-14` + `DEATH_DIFF-1`
##   Res.Df        RSS Df Sum of Sq      F    Pr(>F)    
## 1  53164 4.1052e+10                                  
## 2  53152 4.0622e+10 12   4.3e+08 46.886 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#Cases, Deaths & Population on Cases
data3 = covid.time[,c(2,6,9:36)]
fit1.m3 <- lm(cases_Diff~., data=na.omit(data3))
fit2.m3 <- lm(cases_Diff~1, data=na.omit(data3))

step.m3 = stepAIC(fit2.m3,direction="both",scope=list(upper=fit1.m3,lower=fit2.m3),trace = FALSE)

summary(step.m3)
## 
## Call:
## lm(formula = cases_Diff ~ `CASE_DIFF-7` + `CASE_DIFF-14` + `CASE_DIFF-1` + 
##     `CASE_DIFF-8` + `CASE_DIFF-2` + `CASE_DIFF-9` + `CASE_DIFF-6` + 
##     `CASE_DIFF-12` + `CASE_DIFF-3` + `CASE_DIFF-13` + `CASE_DIFF-4` + 
##     `CASE_DIFF-10` + `CASE_DIFF-5` + `DEATH_DIFF-8` + `DEATH_DIFF-7` + 
##     `DEATH_DIFF-6` + `DEATH_DIFF-9` + `DEATH_DIFF-5` + `DEATH_DIFF-2` + 
##     popData2019 + `CASE_DIFF-11` + `DEATH_DIFF-10` + `DEATH_DIFF-11` + 
##     `DEATH_DIFF-12` + `DEATH_DIFF-13` + `DEATH_DIFF-14` + `DEATH_DIFF-1`, 
##     data = na.omit(data3))
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -53607    -24    -11      0  41083 
## 
## Coefficients:
##                   Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)      1.023e+01  3.934e+00    2.601  0.00930 ** 
## `CASE_DIFF-7`    4.632e-01  4.835e-03   95.807  < 2e-16 ***
## `CASE_DIFF-14`   1.093e-01  3.669e-03   29.774  < 2e-16 ***
## `CASE_DIFF-1`   -5.604e-01  4.263e-03 -131.469  < 2e-16 ***
## `CASE_DIFF-8`    3.303e-01  4.891e-03   67.535  < 2e-16 ***
## `CASE_DIFF-2`   -4.299e-01  4.798e-03  -89.593  < 2e-16 ***
## `CASE_DIFF-9`    1.976e-01  5.031e-03   39.286  < 2e-16 ***
## `CASE_DIFF-6`    5.388e-02  5.052e-03   10.667  < 2e-16 ***
## `CASE_DIFF-12`  -1.201e-01  4.749e-03  -25.291  < 2e-16 ***
## `CASE_DIFF-3`   -2.582e-01  4.973e-03  -51.922  < 2e-16 ***
## `CASE_DIFF-13`  -1.221e-01  4.406e-03  -27.706  < 2e-16 ***
## `CASE_DIFF-4`   -1.464e-01  5.066e-03  -28.899  < 2e-16 ***
## `CASE_DIFF-10`   7.124e-02  4.945e-03   14.405  < 2e-16 ***
## `CASE_DIFF-5`   -8.185e-02  5.129e-03  -15.959  < 2e-16 ***
## `DEATH_DIFF-8`   2.187e+00  1.115e-01   19.613  < 2e-16 ***
## `DEATH_DIFF-7`   1.948e+00  1.025e-01   18.999  < 2e-16 ***
## `DEATH_DIFF-6`   1.272e+00  9.095e-02   13.985  < 2e-16 ***
## `DEATH_DIFF-9`   1.532e+00  1.156e-01   13.252  < 2e-16 ***
## `DEATH_DIFF-5`   6.381e-01  7.119e-02    8.963  < 2e-16 ***
## `DEATH_DIFF-2`   3.329e-01  6.382e-02    5.216 1.83e-07 ***
## popData2019      1.032e-07  2.410e-08    4.282 1.86e-05 ***
## `CASE_DIFF-11`   9.897e-03  4.891e-03    2.024  0.04302 *  
## `DEATH_DIFF-10`  1.281e+00  1.146e-01   11.172  < 2e-16 ***
## `DEATH_DIFF-11`  1.225e+00  1.103e-01   11.112  < 2e-16 ***
## `DEATH_DIFF-12`  1.008e+00  1.020e-01    9.884  < 2e-16 ***
## `DEATH_DIFF-13`  8.632e-01  9.057e-02    9.531  < 2e-16 ***
## `DEATH_DIFF-14`  5.726e-01  7.057e-02    8.114 4.99e-16 ***
## `DEATH_DIFF-1`   1.763e-01  6.419e-02    2.746  0.00604 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 874.1 on 53151 degrees of freedom
## Multiple R-squared:  0.5932, Adjusted R-squared:  0.593 
## F-statistic:  2871 on 27 and 53151 DF,  p-value: < 2.2e-16
#Compare models
anova(step.m2,step.m3)
## Analysis of Variance Table
## 
## Model 1: cases_Diff ~ `CASE_DIFF-7` + `CASE_DIFF-14` + `CASE_DIFF-1` + 
##     `CASE_DIFF-8` + `CASE_DIFF-2` + `CASE_DIFF-9` + `CASE_DIFF-6` + 
##     `CASE_DIFF-12` + `CASE_DIFF-3` + `CASE_DIFF-13` + `CASE_DIFF-4` + 
##     `CASE_DIFF-10` + `CASE_DIFF-5` + `DEATH_DIFF-8` + `DEATH_DIFF-7` + 
##     `DEATH_DIFF-6` + `DEATH_DIFF-9` + `DEATH_DIFF-5` + `DEATH_DIFF-2` + 
##     `CASE_DIFF-11` + `DEATH_DIFF-10` + `DEATH_DIFF-11` + `DEATH_DIFF-12` + 
##     `DEATH_DIFF-13` + `DEATH_DIFF-14` + `DEATH_DIFF-1`
## Model 2: cases_Diff ~ `CASE_DIFF-7` + `CASE_DIFF-14` + `CASE_DIFF-1` + 
##     `CASE_DIFF-8` + `CASE_DIFF-2` + `CASE_DIFF-9` + `CASE_DIFF-6` + 
##     `CASE_DIFF-12` + `CASE_DIFF-3` + `CASE_DIFF-13` + `CASE_DIFF-4` + 
##     `CASE_DIFF-10` + `CASE_DIFF-5` + `DEATH_DIFF-8` + `DEATH_DIFF-7` + 
##     `DEATH_DIFF-6` + `DEATH_DIFF-9` + `DEATH_DIFF-5` + `DEATH_DIFF-2` + 
##     popData2019 + `CASE_DIFF-11` + `DEATH_DIFF-10` + `DEATH_DIFF-11` + 
##     `DEATH_DIFF-12` + `DEATH_DIFF-13` + `DEATH_DIFF-14` + `DEATH_DIFF-1`
##   Res.Df        RSS Df Sum of Sq      F    Pr(>F)    
## 1  53152 4.0622e+10                                  
## 2  53151 4.0608e+10  1  14005776 18.332 1.859e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#Cases, Deaths & Population on Cases
data4 = covid.time[,c(2,7,9:36)]
fit1.m4 <- lm(cases_Diff~., data=na.omit(data4))
fit2.m4 <- lm(cases_Diff~1, data=na.omit(data4))

step.m4 = stepAIC(fit2.m4,direction="both",scope=list(upper=fit1.m4,lower=fit2.m4),trace = FALSE)

summary(step.m4)
## 
## Call:
## lm(formula = cases_Diff ~ `CASE_DIFF-7` + `CASE_DIFF-14` + `CASE_DIFF-1` + 
##     `CASE_DIFF-8` + `CASE_DIFF-2` + `CASE_DIFF-9` + `CASE_DIFF-6` + 
##     `CASE_DIFF-12` + `CASE_DIFF-3` + `CASE_DIFF-13` + `CASE_DIFF-4` + 
##     `CASE_DIFF-10` + `CASE_DIFF-5` + `DEATH_DIFF-8` + `DEATH_DIFF-7` + 
##     `DEATH_DIFF-6` + `DEATH_DIFF-9` + `DEATH_DIFF-5` + `DEATH_DIFF-2` + 
##     `CASE_DIFF-11` + `DEATH_DIFF-10` + `DEATH_DIFF-11` + `DEATH_DIFF-12` + 
##     `DEATH_DIFF-13` + `DEATH_DIFF-14` + `DEATH_DIFF-1`, data = na.omit(data4))
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -53595    -24    -15     -3  41110 
## 
## Coefficients:
##                  Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)     14.572354   3.801912    3.833 0.000127 ***
## `CASE_DIFF-7`    0.464288   0.004828   96.157  < 2e-16 ***
## `CASE_DIFF-14`   0.109556   0.003669   29.858  < 2e-16 ***
## `CASE_DIFF-1`   -0.559992   0.004262 -131.384  < 2e-16 ***
## `CASE_DIFF-8`    0.331329   0.004886   67.818  < 2e-16 ***
## `CASE_DIFF-2`   -0.429274   0.004797  -89.491  < 2e-16 ***
## `CASE_DIFF-9`    0.198530   0.005027   39.491  < 2e-16 ***
## `CASE_DIFF-6`    0.054925   0.005046   10.884  < 2e-16 ***
## `CASE_DIFF-12`  -0.119549   0.004748  -25.180  < 2e-16 ***
## `CASE_DIFF-3`   -0.257402   0.004970  -51.792  < 2e-16 ***
## `CASE_DIFF-13`  -0.121642   0.004406  -27.608  < 2e-16 ***
## `CASE_DIFF-4`   -0.145509   0.005063  -28.742  < 2e-16 ***
## `CASE_DIFF-10`   0.071964   0.004943   14.558  < 2e-16 ***
## `CASE_DIFF-5`   -0.080894   0.005125  -15.785  < 2e-16 ***
## `DEATH_DIFF-8`   2.188295   0.111527   19.621  < 2e-16 ***
## `DEATH_DIFF-7`   1.949829   0.102564   19.011  < 2e-16 ***
## `DEATH_DIFF-6`   1.273209   0.090964   13.997  < 2e-16 ***
## `DEATH_DIFF-9`   1.532828   0.115625   13.257  < 2e-16 ***
## `DEATH_DIFF-5`   0.639008   0.071197    8.975  < 2e-16 ***
## `DEATH_DIFF-2`   0.333297   0.063829    5.222 1.78e-07 ***
## `CASE_DIFF-11`   0.010553   0.004889    2.158 0.030910 *  
## `DEATH_DIFF-10`  1.280985   0.114642   11.174  < 2e-16 ***
## `DEATH_DIFF-11`  1.225222   0.110269   11.111  < 2e-16 ***
## `DEATH_DIFF-12`  1.007917   0.102001    9.881  < 2e-16 ***
## `DEATH_DIFF-13`  0.862914   0.090589    9.526  < 2e-16 ***
## `DEATH_DIFF-14`  0.572329   0.070579    8.109 5.21e-16 ***
## `DEATH_DIFF-1`   0.176808   0.064201    2.754 0.005889 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 874.2 on 53152 degrees of freedom
## Multiple R-squared:  0.5931, Adjusted R-squared:  0.5929 
## F-statistic:  2980 on 26 and 53152 DF,  p-value: < 2.2e-16
#Compare models
anova(step.m3,step.m4)
## Analysis of Variance Table
## 
## Model 1: cases_Diff ~ `CASE_DIFF-7` + `CASE_DIFF-14` + `CASE_DIFF-1` + 
##     `CASE_DIFF-8` + `CASE_DIFF-2` + `CASE_DIFF-9` + `CASE_DIFF-6` + 
##     `CASE_DIFF-12` + `CASE_DIFF-3` + `CASE_DIFF-13` + `CASE_DIFF-4` + 
##     `CASE_DIFF-10` + `CASE_DIFF-5` + `DEATH_DIFF-8` + `DEATH_DIFF-7` + 
##     `DEATH_DIFF-6` + `DEATH_DIFF-9` + `DEATH_DIFF-5` + `DEATH_DIFF-2` + 
##     popData2019 + `CASE_DIFF-11` + `DEATH_DIFF-10` + `DEATH_DIFF-11` + 
##     `DEATH_DIFF-12` + `DEATH_DIFF-13` + `DEATH_DIFF-14` + `DEATH_DIFF-1`
## Model 2: cases_Diff ~ `CASE_DIFF-7` + `CASE_DIFF-14` + `CASE_DIFF-1` + 
##     `CASE_DIFF-8` + `CASE_DIFF-2` + `CASE_DIFF-9` + `CASE_DIFF-6` + 
##     `CASE_DIFF-12` + `CASE_DIFF-3` + `CASE_DIFF-13` + `CASE_DIFF-4` + 
##     `CASE_DIFF-10` + `CASE_DIFF-5` + `DEATH_DIFF-8` + `DEATH_DIFF-7` + 
##     `DEATH_DIFF-6` + `DEATH_DIFF-9` + `DEATH_DIFF-5` + `DEATH_DIFF-2` + 
##     `CASE_DIFF-11` + `DEATH_DIFF-10` + `DEATH_DIFF-11` + `DEATH_DIFF-12` + 
##     `DEATH_DIFF-13` + `DEATH_DIFF-14` + `DEATH_DIFF-1`
##   Res.Df        RSS Df Sum of Sq      F    Pr(>F)    
## 1  53151 4.0608e+10                                  
## 2  53152 4.0622e+10 -1 -14005776 18.332 1.859e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Final Model & Diagnostic Test

summary(step.m3)
## 
## Call:
## lm(formula = cases_Diff ~ `CASE_DIFF-7` + `CASE_DIFF-14` + `CASE_DIFF-1` + 
##     `CASE_DIFF-8` + `CASE_DIFF-2` + `CASE_DIFF-9` + `CASE_DIFF-6` + 
##     `CASE_DIFF-12` + `CASE_DIFF-3` + `CASE_DIFF-13` + `CASE_DIFF-4` + 
##     `CASE_DIFF-10` + `CASE_DIFF-5` + `DEATH_DIFF-8` + `DEATH_DIFF-7` + 
##     `DEATH_DIFF-6` + `DEATH_DIFF-9` + `DEATH_DIFF-5` + `DEATH_DIFF-2` + 
##     popData2019 + `CASE_DIFF-11` + `DEATH_DIFF-10` + `DEATH_DIFF-11` + 
##     `DEATH_DIFF-12` + `DEATH_DIFF-13` + `DEATH_DIFF-14` + `DEATH_DIFF-1`, 
##     data = na.omit(data3))
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -53607    -24    -11      0  41083 
## 
## Coefficients:
##                   Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)      1.023e+01  3.934e+00    2.601  0.00930 ** 
## `CASE_DIFF-7`    4.632e-01  4.835e-03   95.807  < 2e-16 ***
## `CASE_DIFF-14`   1.093e-01  3.669e-03   29.774  < 2e-16 ***
## `CASE_DIFF-1`   -5.604e-01  4.263e-03 -131.469  < 2e-16 ***
## `CASE_DIFF-8`    3.303e-01  4.891e-03   67.535  < 2e-16 ***
## `CASE_DIFF-2`   -4.299e-01  4.798e-03  -89.593  < 2e-16 ***
## `CASE_DIFF-9`    1.976e-01  5.031e-03   39.286  < 2e-16 ***
## `CASE_DIFF-6`    5.388e-02  5.052e-03   10.667  < 2e-16 ***
## `CASE_DIFF-12`  -1.201e-01  4.749e-03  -25.291  < 2e-16 ***
## `CASE_DIFF-3`   -2.582e-01  4.973e-03  -51.922  < 2e-16 ***
## `CASE_DIFF-13`  -1.221e-01  4.406e-03  -27.706  < 2e-16 ***
## `CASE_DIFF-4`   -1.464e-01  5.066e-03  -28.899  < 2e-16 ***
## `CASE_DIFF-10`   7.124e-02  4.945e-03   14.405  < 2e-16 ***
## `CASE_DIFF-5`   -8.185e-02  5.129e-03  -15.959  < 2e-16 ***
## `DEATH_DIFF-8`   2.187e+00  1.115e-01   19.613  < 2e-16 ***
## `DEATH_DIFF-7`   1.948e+00  1.025e-01   18.999  < 2e-16 ***
## `DEATH_DIFF-6`   1.272e+00  9.095e-02   13.985  < 2e-16 ***
## `DEATH_DIFF-9`   1.532e+00  1.156e-01   13.252  < 2e-16 ***
## `DEATH_DIFF-5`   6.381e-01  7.119e-02    8.963  < 2e-16 ***
## `DEATH_DIFF-2`   3.329e-01  6.382e-02    5.216 1.83e-07 ***
## popData2019      1.032e-07  2.410e-08    4.282 1.86e-05 ***
## `CASE_DIFF-11`   9.897e-03  4.891e-03    2.024  0.04302 *  
## `DEATH_DIFF-10`  1.281e+00  1.146e-01   11.172  < 2e-16 ***
## `DEATH_DIFF-11`  1.225e+00  1.103e-01   11.112  < 2e-16 ***
## `DEATH_DIFF-12`  1.008e+00  1.020e-01    9.884  < 2e-16 ***
## `DEATH_DIFF-13`  8.632e-01  9.057e-02    9.531  < 2e-16 ***
## `DEATH_DIFF-14`  5.726e-01  7.057e-02    8.114 4.99e-16 ***
## `DEATH_DIFF-1`   1.763e-01  6.419e-02    2.746  0.00604 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 874.1 on 53151 degrees of freedom
## Multiple R-squared:  0.5932, Adjusted R-squared:  0.593 
## F-statistic:  2871 on 27 and 53151 DF,  p-value: < 2.2e-16
#Diagnostic Test
plot(step.m3,sub.caption = "")

Model Presenting

Model Name Res.DF RSS Df Sum of Sq F Pr(>F)
1 52547 39.17
2 52534 38.78 13 388052910 40.438 <2.2e-16 ***
Model Name Res.DF RSS Df Sum of Sq F Pr(>F)
2 52534 38.78
3 52533 38.77 1 11207507 15.187 9.75e-05 ***
Model Name Res.DF RSS Df Sum of
3 52533 38.77
4 52534 38.78 -1 -11207507 15.187 9.75e-05 ***
stargazer(step.m1, step.m2, step.m3, type = "text", title = "Results of Model 1 & 2 & 3", align = T)
## 
## Results of Model 1 & 2 & 3
## =============================================================================================================
##                                                        Dependent variable:                                   
##                     -----------------------------------------------------------------------------------------
##                                                            cases_Diff                                        
##                                  (1)                           (2)                           (3)             
## -------------------------------------------------------------------------------------------------------------
## `CASE_DIFF-7`                 0.489***                      0.464***                      0.463***           
##                                (0.005)                       (0.005)                       (0.005)           
##                                                                                                              
## `CASE_DIFF-14`                0.114***                      0.110***                      0.109***           
##                                (0.004)                       (0.004)                       (0.004)           
##                                                                                                              
## `CASE_DIFF-1`                 -0.552***                     -0.560***                     -0.560***          
##                                (0.004)                       (0.004)                       (0.004)           
##                                                                                                              
## `CASE_DIFF-8`                 0.357***                      0.331***                      0.330***           
##                                (0.005)                       (0.005)                       (0.005)           
##                                                                                                              
## `CASE_DIFF-2`                 -0.420***                     -0.429***                     -0.430***          
##                                (0.005)                       (0.005)                       (0.005)           
##                                                                                                              
## `CASE_DIFF-9`                 0.212***                      0.199***                      0.198***           
##                                (0.005)                       (0.005)                       (0.005)           
##                                                                                                              
## `CASE_DIFF-6`                 0.070***                      0.055***                      0.054***           
##                                (0.005)                       (0.005)                       (0.005)           
##                                                                                                              
## `CASE_DIFF-12`                -0.118***                     -0.120***                     -0.120***          
##                                (0.005)                       (0.005)                       (0.005)           
##                                                                                                              
## `CASE_DIFF-3`                 -0.254***                     -0.257***                     -0.258***          
##                                (0.005)                       (0.005)                       (0.005)           
##                                                                                                              
## `CASE_DIFF-13`                -0.118***                     -0.122***                     -0.122***          
##                                (0.004)                       (0.004)                       (0.004)           
##                                                                                                              
## `CASE_DIFF-4`                 -0.146***                     -0.146***                     -0.146***          
##                                (0.005)                       (0.005)                       (0.005)           
##                                                                                                              
## `CASE_DIFF-10`                0.078***                      0.072***                      0.071***           
##                                (0.005)                       (0.005)                       (0.005)           
##                                                                                                              
## `CASE_DIFF-5`                 -0.074***                     -0.081***                     -0.082***          
##                                (0.005)                       (0.005)                       (0.005)           
##                                                                                                              
## `DEATH_DIFF-8`                                              2.188***                      2.187***           
##                                                              (0.112)                       (0.112)           
##                                                                                                              
## `DEATH_DIFF-7`                                              1.950***                      1.948***           
##                                                              (0.103)                       (0.103)           
##                                                                                                              
## `DEATH_DIFF-6`                                              1.273***                      1.272***           
##                                                              (0.091)                       (0.091)           
##                                                                                                              
## `DEATH_DIFF-9`                                              1.533***                      1.532***           
##                                                              (0.116)                       (0.116)           
##                                                                                                              
## `DEATH_DIFF-5`                                              0.639***                      0.638***           
##                                                              (0.071)                       (0.071)           
##                                                                                                              
## `DEATH_DIFF-2`                                              0.333***                      0.333***           
##                                                              (0.064)                       (0.064)           
##                                                                                                              
## popData2019                                                                              0.00000***          
##                                                                                           (0.00000)          
##                                                                                                              
## `CASE_DIFF-11`                0.014***                       0.011**                       0.010**           
##                                (0.005)                       (0.005)                       (0.005)           
##                                                                                                              
## `DEATH_DIFF-10`                                             1.281***                      1.281***           
##                                                              (0.115)                       (0.115)           
##                                                                                                              
## `DEATH_DIFF-11`                                             1.225***                      1.225***           
##                                                              (0.110)                       (0.110)           
##                                                                                                              
## `DEATH_DIFF-12`                                             1.008***                      1.008***           
##                                                              (0.102)                       (0.102)           
##                                                                                                              
## `DEATH_DIFF-13`                                             0.863***                      0.863***           
##                                                              (0.091)                       (0.091)           
##                                                                                                              
## `DEATH_DIFF-14`                                             0.572***                      0.573***           
##                                                              (0.071)                       (0.071)           
##                                                                                                              
## `DEATH_DIFF-1`                                              0.177***                      0.176***           
##                                                              (0.064)                       (0.064)           
##                                                                                                              
## Constant                      15.682***                     14.572***                     10.232***          
##                                (3.821)                       (3.802)                       (3.934)           
##                                                                                                              
## -------------------------------------------------------------------------------------------------------------
## Observations                   53,179                        53,179                        53,179            
## R2                              0.589                         0.593                         0.593            
## Adjusted R2                     0.589                         0.593                         0.593            
## Residual Std. Error     878.732 (df = 53164)          874.216 (df = 53152)          874.074 (df = 53151)     
## F Statistic         5,436.861*** (df = 14; 53164) 2,979.502*** (df = 26; 53152) 2,870.764*** (df = 27; 53151)
## =============================================================================================================
## Note:                                                                             *p<0.1; **p<0.05; ***p<0.01
stargazer(step.m3, step.m4, type = "text", title = "Results of Model 3 & 4", align = T)
## 
## Results of Model 3 & 4
## ===============================================================================
##                                         Dependent variable:                    
##                     -----------------------------------------------------------
##                                             cases_Diff                         
##                                  (1)                           (2)             
## -------------------------------------------------------------------------------
## `CASE_DIFF-7`                 0.463***                      0.464***           
##                                (0.005)                       (0.005)           
##                                                                                
## `CASE_DIFF-14`                0.109***                      0.110***           
##                                (0.004)                       (0.004)           
##                                                                                
## `CASE_DIFF-1`                 -0.560***                     -0.560***          
##                                (0.004)                       (0.004)           
##                                                                                
## `CASE_DIFF-8`                 0.330***                      0.331***           
##                                (0.005)                       (0.005)           
##                                                                                
## `CASE_DIFF-2`                 -0.430***                     -0.429***          
##                                (0.005)                       (0.005)           
##                                                                                
## `CASE_DIFF-9`                 0.198***                      0.199***           
##                                (0.005)                       (0.005)           
##                                                                                
## `CASE_DIFF-6`                 0.054***                      0.055***           
##                                (0.005)                       (0.005)           
##                                                                                
## `CASE_DIFF-12`                -0.120***                     -0.120***          
##                                (0.005)                       (0.005)           
##                                                                                
## `CASE_DIFF-3`                 -0.258***                     -0.257***          
##                                (0.005)                       (0.005)           
##                                                                                
## `CASE_DIFF-13`                -0.122***                     -0.122***          
##                                (0.004)                       (0.004)           
##                                                                                
## `CASE_DIFF-4`                 -0.146***                     -0.146***          
##                                (0.005)                       (0.005)           
##                                                                                
## `CASE_DIFF-10`                0.071***                      0.072***           
##                                (0.005)                       (0.005)           
##                                                                                
## `CASE_DIFF-5`                 -0.082***                     -0.081***          
##                                (0.005)                       (0.005)           
##                                                                                
## `DEATH_DIFF-8`                2.187***                      2.188***           
##                                (0.112)                       (0.112)           
##                                                                                
## `DEATH_DIFF-7`                1.948***                      1.950***           
##                                (0.103)                       (0.103)           
##                                                                                
## `DEATH_DIFF-6`                1.272***                      1.273***           
##                                (0.091)                       (0.091)           
##                                                                                
## `DEATH_DIFF-9`                1.532***                      1.533***           
##                                (0.116)                       (0.116)           
##                                                                                
## `DEATH_DIFF-5`                0.638***                      0.639***           
##                                (0.071)                       (0.071)           
##                                                                                
## `DEATH_DIFF-2`                0.333***                      0.333***           
##                                (0.064)                       (0.064)           
##                                                                                
## popData2019                  0.00000***                                        
##                               (0.00000)                                        
##                                                                                
## `CASE_DIFF-11`                 0.010**                       0.011**           
##                                (0.005)                       (0.005)           
##                                                                                
## `DEATH_DIFF-10`               1.281***                      1.281***           
##                                (0.115)                       (0.115)           
##                                                                                
## `DEATH_DIFF-11`               1.225***                      1.225***           
##                                (0.110)                       (0.110)           
##                                                                                
## `DEATH_DIFF-12`               1.008***                      1.008***           
##                                (0.102)                       (0.102)           
##                                                                                
## `DEATH_DIFF-13`               0.863***                      0.863***           
##                                (0.091)                       (0.091)           
##                                                                                
## `DEATH_DIFF-14`               0.573***                      0.572***           
##                                (0.071)                       (0.071)           
##                                                                                
## `DEATH_DIFF-1`                0.176***                      0.177***           
##                                (0.064)                       (0.064)           
##                                                                                
## Constant                      10.232***                     14.572***          
##                                (3.934)                       (3.802)           
##                                                                                
## -------------------------------------------------------------------------------
## Observations                   53,179                        53,179            
## R2                              0.593                         0.593            
## Adjusted R2                     0.593                         0.593            
## Residual Std. Error     874.074 (df = 53151)          874.216 (df = 53152)     
## F Statistic         2,870.764*** (df = 27; 53151) 2,979.502*** (df = 26; 53152)
## ===============================================================================
## Note:                                               *p<0.1; **p<0.05; ***p<0.01